Descriptive Statistics, Correlation, Regression Analysis

1
ASSIGNMENT- QUANTITATIVE RESEARCH
Question 1: Descriptive statistics
The descriptive analysis of the data is provided on the table below. The measures of
central tendency are mean, median and mode. The mean gives the average value for each
variable, while the median is a single number that represents the center of the data set. The
mode indicates the value with the highest frequency for each variable. The measures of
dispersion are range and standard deviation. The range gives the difference of the maximum
and the minimum value for each variable. The standard deviation indicated how dispersed the
data points of each variable are spread out from the mean.
Statistics
WAGE HOURS IQ KWW EDUC EXPER
TENUR
E AGE SIBS MEDUC FED
N Valid 479 479 479 479 479 479 479 479 479 479
Missing 0 0 0 0 0 0 0 0 0 0
Mean 1007.994 44.422 103.816 36.706 13.743 11.628 7.332 33.025 2.754 10.983 10
Median 962.000 40.000 105.000 37.000 13.000 11.000 7.000 33.000 2.000 12.000 11
Mode 1000.0 40.0 109.0 38.0 12.0 9.0 1.0 30.0 1.0 12.0
Std. Deviation 411.5006 7.1181 14.2482 7.4482 2.2358 4.1534 5.0970 3.0852 2.2016 2.6402 3.
Skewness 1.069 1.612 -.213 -.296 .412 .084 .410 .156 1.765 -.378
Range 2571.0 53.0 86.0 43.0 9.0 21.0 22.0 10.0 14.0 17.0
Minimum 200.0 27.0 59.0 13.0 9.0 1.0 .0 28.0 .0 1.0
Maximum 2771.0 80.0 145.0 56.0 18.0 22.0 22.0 38.0 14.0 18.0
There are 479 observations in this data set. The mean wage (monthly earnings) is
$1,007.99, while the median wage is $962.00. Hence, the data appears to be skewed to the
right, since the mean is greater than the median of wage. The skewness statistic is 1.069
which indicates that the wage data is very slightly skewed to the right. The range in the
variable is $2,571.00, with the highest monthly earnings being $2,771.00 and the lowest
monthly earnings being $200.00. The standard deviation for wage is 411.50, which means
that data is highly dispersed from its mean.
The mean hours is 44.42hours. The skewness is at 1.61, which indicates that the hours
data is highly skewed to the right, which means most of the data is close to the maximum
value. The range for the hours variable is 53 hours, with the lowest value being 27 hours and
the highest value being 80 hours.

2
For the IQ variable, the mean is 103.82, the median is 105.00, and the mode is 109.00.
the range is 86.0, with the maximum value being 145.0 and the minimum value being 59.0.
Question 2: Correlation
The correlation table helps in finding out what variables affect Wage and how they affect
the wage. First, we find the correlation between all the variables and wage, using the
correlation matrix. The test is to see whether there is a relationship between each variable and
wage. Therefore, the hypothesis test is:
(No, the variable has no relationship with wage)
(Yes, the variable has a relationship with wage).
The decision rule is to reject if the significance is less than 0.05, and fail to reject
, when the significance is greater than 0.05.
If the test result is Yes, then we explain the nature of the relationship between the
variable and wage. First, if its positive or negative, based on the sign on the value of r. Next,
the value of r indicates the magnitude of the relationship. The table below indicate the criteria
used to determine the strength of the relationship between a variable and wage.
Magnitude of relationship Value of r
0.51 to 1.0, -0.51 to -1.0 Strong
0.31 to 0.5, -0.31 to -0.5 Moderate
0.11 to 0.3, -0.11 to -0.3 Weak
-0.1 to 0.1 None, or Very weak
The results for the correlation matrix are shown in the table below.
WAGE Relationship (Strength, Directions and Test results)
WAGE Pearson Correlation 1
Sig. (2-tailed)
HOURS Pearson Correlation -.030
Sig. (2-tailed) .516 >0.05, Fail to reject Ho. No relationship.
IQ Pearson Correlation .298** Moderate, positive relationship
Sig. (2-tailed) .000 <0.05, Reject Ho; Yes relationship.
KWW Pearson Correlation .340** Strong, positive relationship

3
Sig. (2-tailed) .000 <0.05, Reject Ho; Yes relationship.
EDUC Pearson Correlation .331** Strong, positive relationship
Sig. (2-tailed) .000 <0.05, Reject Ho; Yes relationship.
EXPER Pearson Correlation -.029
Sig. (2-tailed) .531 >0.05, Fail to reject Ho. No relationship.
TENURE Pearson Correlation .111* Weak, positive relationship
Sig. (2-tailed) .015 <0.05, Reject Ho; Yes relationship.
AGE Pearson Correlation .161** Weak, positive relationship
Sig. (2-tailed) .000 <0.05, Reject Ho; Yes relationship.
SIBS Pearson Correlation -.120** Weak, negative relationship
Sig. (2-tailed) .009 <0.05, Reject Ho; Yes relationship.
MEDUC Pearson Correlation .224** Weak, positive relationship
Sig. (2-tailed) .000 <0.05, Reject Ho; Yes relationship.
FEDUC Pearson Correlation .264** Weak, positive relationship
Sig. (2-tailed) .000 <0.05, Reject Ho; Yes relationship.
From the correlation matrix above, we find that the variables with a significant
relationship with wage at 0.05 significance level are IQ, KWW, educ, tenure, age, sibs,
meduc, feduc. Of these, only KWW and educ have a strong relationship with wage.
Question 3: Regression
We start with a simple regression, where we regress wage on education.
Variables Entered/Removeda
Model
Variables
Entered
Variables
Removed Method
1 EDUCb . Enter
a. Dependent Variable: WAGE
b. All requested variables entered.

4
The results are shown in the table below. The regression model follows the format:
. The R-square for this model is 0.110*100%=11.0%. Thus, 11% of the
variation in monthly earning (wage) is explained by years of education (educ).
The F-Test is not explained for a simple model where we have one independent
variable.The table below gives the coefficients for the simple regression model above.
The significance level for the independent variable is 0.00 < 0.05, hence there is a
significant relationship between educ and wage, with a coefficient of . The
constant coefficient is . Therefore, the regression model becomes:
Hence, one more year of education increases the wage by $60.93, while a person with
zero years of education is expected to earn $170.60 monthly.
Effect:
If the years of education increase by two, the wage will increase by $121.86 (that is,
$60.93*2 years). If the years of education increase by five, the wage will increase by $304.65
(that is, $60.93*5 years).
Prediction:
The predicated wage for a person with 18 years of education, is found as:
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of
the Estimate
1 .331a .110 .108 388.7030
a. Predictors: (Constant), EDUC
Coefficientsa
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.B Std. Error Beta
1 (Constant) 170.596 110.719 1.541 .124
EDUC 60.932 7.952 .331 7.663 .000
a. Dependent Variable: WAGE